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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unbounded composition operators on $ H\sp 2(B\sb 2)$


Authors: J. A. Cima and W. R. Wogen
Journal: Proc. Amer. Math. Soc. 99 (1987), 477-483
MSC: Primary 32A35; Secondary 47B38
MathSciNet review: 875384
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Abstract: Examples are given of holomorphic self-maps of the unit ball on $ {{\text{C}}^2}$ which induce unbounded composition operators on the Hardy space $ {H^2}$. In particular, an example is given which is one-to-one on the closed ball. Also, a valence condition on the boundary of this ball is given which is sufficient for unboundedness of the induced composition operator.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0875384-4
Keywords: Hardy spaces, composition operators, holomorphic mappings
Article copyright: © Copyright 1987 American Mathematical Society